Are good mathematicians merely good at memorizing math formulas? 
Answer by Alan Bustany on Quora. 


Far from it! The typical good mathematician cannot remember many formulae at all, and is usually rather poor at mental arithmetic.

The beauty of Mathematics is that you don't have to remember a whole bunch of apparently disconnected facts. Almost everything is connected. Not only that, but it is logically connected. You can derive most things from relatively few fundamental principles.

Repeated use of certain equations do result in them sticking in memory. For example every good mathematician, and lots of not so good ones, knows the quadratic formula for the roots of the quadratic equation $ax^2+bx+c=0$, namely:

$ x=\frac{-b\pm\sqrt{b^2–4ac}}{2a}$

But a good mathematician would not dream of memorizing this formula without understanding how it is derived by, for example, completing the square. Someone who merely memorizes the formula so that they can, for example, pass an exam is not destined to be a good mathematician, I can assure you.